The effect of supply uncertainty/quality considerations on inventory control has been widely recognized (see Wright and Mehrez, 1998; Yano and Lee, 1995, for related reviews). Different assumptions concerning the uncertain supply process have been made. One stream of research considers a ‘‘stochastically proportional’’ supply where the fraction of imperfect quality items in a lot is random with a known probability distribution independent of the order quantity. Earlier work in this stream includes Karlin (1958), Shih (1980), and Silver (1976). Recent related research includes the work of Salameh and Jaber (2000) who assume that a screening process is initiated upon the receipt of an order where imperfect items are detected to be sold later at a discount. Several authors recently adopt Salameh and Jaber’s assumptions on handling of imperfect quality.